This would be beyond great. I'm guessing that Butler has realized he's stuck playing here for $4m this year and nothing's really gonna change that - he will be paid a lot more starting next year but there's no way he gets more THIS year unless he works out an extension with the Pats. I'm guessing he probably would prefer to stay here long-term over a team he's not familiar with, so perhaps he has decided that it makes sense for him to get more than $4m right now and some longer term security, and know he's staying in one spot for a while, even if it means making a little less in the long run. 4/$42 starting today may feel better than 4/$52 somewhere else starting 1 year from today.
Further, it means he hits UFA again a year sooner, so if he starts out on a 4 year deal right now, he'll be just barely 31 the next time he is coming up on free agency. Not "old" yet but he may command a little more money at that time if he's one year younger.
From that perspective, if he stays here on 1/$4m and then signs for 4/$52m next year elsewhere, that's $56m over 5 years. But if he starts on a 4/$42m deal today, he's made less than he would've on the other deal, but after 4 years he can sign a new deal at the then-current market prices for CBs. If he can get $12m a year at that time (seems plausible considering his talent, age, and the salary cap increases year-over-year), then he's made $54m across that same 5 year time period, barely less money than in the first scenario, and he gets to stay put in NE.